Sample Size for Test of Paired Means

Example clinical scenario

Systolic blood pressure is measured in the same patients before and after an eight-week lifestyle intervention to detect a meaningful mean within-person change.

Formula and methodological note

The calculator uses the normal-approximation paired-mean formula based on the standard deviation of within-participant differences, the selected alternative, Type I error, and power. The result is rounded up to complete pairs before the dropout/non-response adjustment.

It assumes that measurements are correctly paired within participants, the paired differences are independent across participants and approximately normally distributed, and the SDdiff and detectable difference use the same outcome units.

It does not account for more than two measurements, clustering, design effects, missing outcome patterns, non-normal paired differences, non-inferiority/equivalence designs, or interim monitoring.

Method references

1. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman and Hall/CRC; 2017.
2. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988.